Question

A wire is in the form of a square of side 16cm.it is bent to make a rectangle of breadth 10cm.find the lenght of the rectangle formed. Find which one has more area

Answer 1

Given :

•Side of a square =16cm

• Breadth of a rectangle =10cm

To find :

•The length of the rectangle =?

Formula :

$\bullet \sf \: area \: of \: square = {(side)}^{2}$

$\\ \bullet \sf \: area \: of \:rectangle = l \times b$

Solution :

$\\ \therefore \sf \: area \: of \: square = area \: of \: rectangle \\ \\ \\ \implies \sf \: {(side)}^{2} = l \times b \\ \\ \\ \implies \sf \: {(16)}^{2} = 10 \times l \\ \\ \\ \implies \sf \: 256 = 10 \times l \\ \\ \\ \implies \sf \: l = \frac{256}{10} \\ \\ \\ \implies \sf \:l = 25.6cm$

• The value of length is 25.6cm

Answer 2

${\large{\rm{\underline{Let's \: understand \: the \: question \: 1^{st}}}}}$

${\bull}$ This question says that there is a wire is in the form of a square of side 16cm. It is bent to make a rectangle of breadth 10cm .We have to find the lenght of the rectangle formed. And we also have to find that which one has more area (rectangle or square) ?

${\large{\rm{\underline{Given \; that}}}}$

${\longrightarrow}$ Wire is in the shape of square and it's side is 16 cm.

${\longrightarrow}$ Now, square shape wire is bent to make a rectangle of breadth 10 cm

${\large{\rm{\underline{To \; find}}}}$

${\longrightarrow}$ Length of formed rectangle

${\longrightarrow}$ Which one has more area.

${\large{\rm{\underline{Solution}}}}$

${\longrightarrow}$ Length of formed rectangle = 22 cm

${\longrightarrow}$ Square has more area.

${\large{\rm{\underline{Using \; concepts}}}}$

${\longrightarrow}$ Formula to find area of rectangle

${\longrightarrow}$ Formula to find area of square

${\longrightarrow}$ Formula to find perimeter of square

${\longrightarrow}$ Formula to find perimeter of rectangle

${\large{\rm{\underline{formulas}}}}$

${\longrightarrow}$ Area of rectangle = Length × Breadth

${\longrightarrow}$ Area of square = Side × Side

${\longrightarrow}$ Perimeter of square = 4 × side

${\longrightarrow}$ Perimeter of rectangle = 2(l+b)

${\large{\rm{\underline{Full \; Solution}}}}$

~ Let's find the length of rectangle

↗ Given side (square) = 16 cm.

↗ Perimeter of square = 4 × side

↗ Perimeter of square = 4 × 16

↗ Perimeter of square = 64 cm

${\pink{\frak{Henceforth, \: 64 \: cm \: is \: perimeter \: of \: square}}}$

~ According to the question, a wire is in the form of a square. It is bent to make a rectangle.

Means,

↗ Perimeter of square = Perimeter of rectangle

↗ 64 = 2(l+b)

↗ 64 = 2(l+10)

↗ 64 = 2l + 20

↗ 64 - 20 = 2l

↗ 44 = 2l

↗ 44/2 = l

↗ 22 = l

↗ l = 22 cm

${\pink{\frak{Henceforth, \: 22 \: cm \: is \: length \: of \: rectangle}}}$

~ Let's find the area of square and rectangle.

☑ Area for square

↗ Area of square = Side × Side

↗ Area of square = 16 × 16

↗ Area of square = 256 cm²

${\pink{\frak{Henceforth, \: 256 \: cm^{2} \: is \: area \: of \: square}}}$

☑ Area for rectangle

↗ Area of rectangle = L × B

↗ Area of rectangle = 22 × 10

↗ Area of rectangle = 220 cm²

${\pink{\frak{Henceforth, \: 220 \: cm^{2} \: is \: area \: of \: rectangle}}}$

~ Now let's find which one has more area.

↗ Area of rectangle and Area of square

↗ 220 cm² and 256 cm²

↗ 220 cm² < 256 cm²

↗ Area of rectangle < Area of square

${\pink{\frak{Henceforth, \: area \: of \: square \: has \: more \: area}}}$